No, Puirt-a-Beul is one of many mouth music traditions. There is no logical connection between them. Just as flute and bagpipe traditions exist all (?) over the world.
It's misleading to simply lump a whole mass of different cultures together, IMO. It's even further wide of the mark to claim "it's a culture living by itself".
If you want to discuss some aspect of mouth music then post something more specific . . Some of the clever souls round here are then bound to add links to past discussions of interest. (Otherwise you can go and investigate the Mudcat search facilities, but that can be a bit "heavy" at first!)
Welcome, anyway!
George